A GENERALIZATION ON THE NTH COMMUTATIVITY DEGREE OF ALTERNATING GROUPS OF DEGREE 4 AND 5

Authors

  • Norarida Abd Rhani Faculty of Computer and Mathematical Sciences, Universiti Teknologi MARA, 40450 Shah Alam, Selangor, Malaysia
  • Nor Muhainiah Mohd Ali Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia, 81310 UTM Johor Bahru, Johor, Malaysia
  • Nor Haniza Sarmin Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia, 81310 UTM Johor Bahru, Johor, Malaysia

DOI:

https://doi.org/10.11113/jt.v78.7813

Keywords:

Abelianness, commutativity degree, alternating group

Abstract

The theory of commutativity degree is important in determining the abelianness of a group. The commutativity degree of a finite group G is the probability that a pair of elements chosen randomly from a group G, commute. The concept of commutativity degree can be generalized to the nth commutativity degree of a group which is defined as the probability of commuting the nth power of a randomly chosen element with another random element from the same group. In this research, the nth commutativity degree of alternating groups of degree 4 and 5 are presented.

References

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(5) N. M. Mohd Ali, N. H. Sarmin. 2010. On some problem in group theory of probabilistic nature. Menemui Matematik. 32(2): 35-41.

(6) J. B. Fraleigh. 2000. A First Course in Abstract Algebra. Addision Wesley Longman, Inc.

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Published

2016-03-09

Issue

Vol. 78 No. 3-2: Steering Innovation, Serving Society in Achieving Global Excellence Towards Science and Technology Vol. 2

Section

Science and Engineering

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Copyright of articles that appear in Jurnal Teknologi belongs exclusively to Penerbit Universiti Teknologi Malaysia (Penerbit UTM Press). This copyright covers the rights to reproduce the article, including reprints, electronic reproductions, or any other reproductions of similar nature.

How to Cite

A GENERALIZATION ON THE NTH COMMUTATIVITY DEGREE OF ALTERNATING GROUPS OF DEGREE 4 AND 5. (2016). Jurnal Teknologi, 78(3-2). https://doi.org/10.11113/jt.v78.7813